5 citations · 13 across the 9 of their papers we have counts for
9 papers
Multiple Horn problems for planar networks and invertible matrices
Anton Alekseev, Arkady Berenstein, Anfisa Gurenkova +1
The multiplicative multiple Horn problem is asking to determine possible singular values of the combinations and for a triple of invertible matrices with giv…
Polynomial integrable systems from cluster structures
Yanpeng Li, Yu Li, Jiang-Hua Lu
We present a general framework for constructing polynomial integrable systems on linearizations of Poisson varieties that admit log-canonical systems. Our construction is in partic…
Action-angle coordinates on coadjoint orbits and multiplicity free spaces from partial tropicalization
Anton Alekseev, Benjamin Hoffman, Jeremy Lane +1
Coadjoint orbits and multiplicity free spaces of compact Lie groups are important examples of symplectic manifolds with Hamiltonian groups actions. Constructing action-angle variab…
Geometric Multiplicities
Arkady Berenstein, Yanpeng Li
In this paper, we introduce geometric multiplicities, which are positive varieties with potential fibered over the Cartan subgroup of a reductive group . They form a monoida…
Concentration of symplectic volumes on Poisson homogeneous spaces
Anton Alekseev, Benjamin Hoffman, Jeremy Lane +1
For a compact Poisson-Lie group , the homogeneous space carries a family of symplectic forms , where is in the positive Weyl chamber and $s…
Langlands Duality and Poisson-Lie Duality via Cluster Theory and Tropicalization
Anton Alekseev, Arkady Berenstein, Benjamin Hoffman +1
Let be a connected semisimple Lie group. There are two natural duality constructions that assign to it the Langlands dual group and the Poisson-Lie dual group . T…
The Gelfand-Zeitlin system as a tropical limit of Ginzburg-Weinstein diffeomorphisms
Anton Alekseev, Jeremy Lane, Yanpeng Li
We show that the Ginzburg-Weinstein diffeomorphism of Alekseev-Meinrenken admits a scaling tropical limit on an open dense subset of $\mathfrak{u}(n)…
Poisson Structures and Potentials
Anton Alekseev, Arkady Berenstein, Benjamin Hoffman +1
We introduce a notion of weakly log-canonical Poisson structures on positive varieties with potentials. Such a Poisson structure is log-canonical up to terms dominated by the poten…
Double Principal Bundles
Honglei Lang, Yanpeng Li, Zhangju Liu
We define double principal bundles (DPBs), for which the frame bundle of a double vector bundle, double Lie groups and double homogeneous spaces are basic examples. It is shown tha…